Question: Solve for $x$ and $y$ using elimination. ${x+6y = 22}$ ${-x-5y = -19}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x+6y = 22}\thinspace$ to find $x$ ${x + 6}{(3)}{= 22}$ $x+18 = 22$ $x+18{-18} = 22{-18}$ ${x = 4}$ You can also plug ${y = 3}$ into $\thinspace {-x-5y = -19}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(3)}{= -19}$ ${x = 4}$